Angle Detection of Input Reference Space Vector

The last issue concerning space vector modulation is the method used to define the angle θ^swi of the input current reference space vector ii,ref or input switching function space vector swi

defined in (3.1-12) and (3.3-2), respectively. As discussed after (3.3-19), input fundamental displacement angle values ϕ^i,1 ≠ 0 lead to the limited voltage transfer ratio. Thus, it is again assumed that ϕ^i,1 = 0, so that the aim is to generate the input reference angle θ^swi synchronised to supply voltage, i.e. θ^{swi =} ω^it.

The synchronisation method used in [P1]–[P7] is based on the zero crossing detection of supply phase voltage ua fundamental component ua,1 and a phase-locked loop (PLL). The system is discussed briefly in [P3] and its basics are presented more extensively e.g. in [Kau97]. The block diagram of the angle detection system is presented in Figure 3.9.

As presented in Figure 3.9, the input reference vector angle θ^swi is based on the phase angle θ^ua,1 of the fundamental supply phase voltage ua,1. The fundamental component ua,1 is attained by low-pass filtering the supply phase voltage ua. The difference between the zero crossing

Matrix Converter Control 45 times of the fundamental voltage ua,1 and its estimated phase angle θ^ua,1 is controlled by a discrete-time proportional-integral (PI) controller tending to produce zero error. The output of the PI controller is the angle increment Δθ^ua,1, which is also the reference for the angular frequency of the input reference vector. At every sample time, the increment Δθ^ua,1 is added to the previous sample time value of angle θ^ua,1. A new value of increment Δθ^ua,1 is got after

Performed in every calculation period Performed after zero crossings

Figure 3.9 Detection of supply phase angle θua,1 using phase-locked loop (PLL) and forming of input reference angle θswi.

The angle θ^ua,1 contains the delay or phase displacement caused by low-pass filtering of ua. However, that delay or phase displacement can be compensated with a constant value θ^{f, as} shown in Figure 3.9, because the filter parameters and the fundamental supply frequency are known. The final input reference angle θ^swi is got after the subtraction of π/2 to compensate the difference between the phase angles of the fundamental voltage ua,1 and the supply voltage fundamental space vector. After that, it is possible to take into account the input displacement angle ϕ^i,1 later in the control system whenever required.

The PLL-based system presented is basically similar to the synchronisation methods suggested in [Nie96a], [Cas98b], [Bla02], [Liu03] and [Liu04]. In all of them, the input voltages are measured and used as the basis of the input reference vector angle instead of the supply voltage as here. This choice has been made to secure the synchronisation because the supply voltages are evidently less distorted than the input voltage and it is also the method used with the current source converters in [Sal02]. In addition [Nie96a], [Cas98b], [Bla02], [Liu03] and [Liu04] deal with the DMC, where the loss of synchronisation is not as fatal as in the IMC, in which the loss of synchronisation reverses the polarity of the dc link voltage, which short-circuits the input capacitors via the ILB diodes.

Compared to methods which measure the supply or input voltages and calculate the voltage space vector, the PLL-based system is simpler and, as shown in [Liu03] and [Liu04], the MC system is also stable in all operation conditions, unlike a system in which the input vector angle follows the input voltage angle directly [Cas02], [Cas04], [Cas05]. Thus, the PLL-based input current reference angle θ^swi always tends to produce sinusoidal input currents [Cas98b], [Bla02]. However, this relates to the angle θ^swi only. The input current produced depends on the load current, as shown in (3.2-3) and in [P4].

3.4 Conclusion

The basics of MC modulation and the derivation of the SVM method for the MCs have been presented in this chapter. The space vector theory has also been introduced briefly as background. In addition, different SVM methods have been compared, concentrating on the common-mode voltages. At the end of the chapter, the synchronisation of the MC operation to the supply has been described with a brief comparison with some other methods suggested in the literature.

The basic operation of the MCs can be modelled and analysed with switching matrices. Due to the requirement of reasonable and safe operation, the number of possible switching states is reduced from the theoretical maximum of 512 to 27 in the MCs. These allowed switching states have conventionally been arranged in three main groups, of which two, including 21 switching states, are used in the SVM modulation. It has been found that several different modulation methods for the MCs have been suggested. The modulation methods can be divided basically into the carrier wave based methods, the SVM methods and the methods combining modulation and the control of load. On the other hand, the modulation methods can be divided into the methods in which the MC is considered to have separate rectification and inverter stages, i.e. the IMC approach, and the methods in which the dependences between the input and the output are defined directly, i.e. the DMC approach.

The basic modulation method used in this thesis is the CSVM, the derivation of which has been presented applying the ideal IMC [P1]–[P7]. The order of the CSVM pulse pattern has been set to minimise the number of switchings with as simple modulator logic as possible. The CSVM has been used as a basic method and three other SVM methods have been presented so that the pulse patterns of the CSVM are arranged and divided differently in the modulation period. The comparison of the common-mode voltages produced by different SVM methods has shown that the CSVM is not the most optimal SVM method but its switching losses should be the second smallest and it can be implemented using the simplest logic among the compared methods.

It has been found that the synchronisation of the input current reference vector of an MC to the input or supply voltage has been studied using different approaches. Those studies have been presented that the synchronisation methods based on the PLL are robust and they can also be implemented easily. Thus, the PLL-based synchronisation has also been used in this thesis [P1]–[P7].

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